Vortex lattice solitons supported by localized gain

We show that localized gain supports the existence of dissipative vortex solitons in periodic Kerr media with strong two-photon absorption. Vortex solitons exist in both focusing and defocusing media, with their propagation constants emerging from semi-infinite or finite gaps in the lattice spectrum. Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles.     

Rotating vortex solitons supported by localized gain

We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.     

Two-dimensional dissipative solitons supported by localized gain

We show that the balance between localized gain and nonlinear cubic dissipation in the two-dimensional nonlinear Schr?dinger equation allows for the existence of stable localized modes that we identify as solitons. Such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. Above the critical value of the gain, symmetry breaking occurs and asymmetric dissipative solitons emerge.     

Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.     

Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices

We introduce a discrete lossy system, into which a double “hot spot” (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic waveguides, with a pair of amplified nonlinear cores embedded into it. We focus on the case of self-defocusing nonlinearity and cubic losses acting at the HSs. Symmetric localized modes pinned to the double HS are constructed in an implicit analytical form, which is done separately for the cases of odd and even numbers of intermediate sites between the HSs. In the former case, some stationary solutions feature a W-like shape, with a low peak at the central site, added to tall peaks at the positions of the embedded HSs. The special case of two adjacent HSs is considered too. Stability of the solution families against small perturbations is investigated in a numerical form, which reveals stable and unstable subfamilies. The instability generated by an isolated positive eigenvalue leads to a spontaneous transformation into a co-existing stable antisymmetric mode, while a pair of complex-conjugate eigenvalues gives rise to persistent breathers. This article is a contribution to the volume dedicated to Professor Helmut Brand on the occasion of his 60th birhday.     

Dechanneling by twins

Twinned regions in Si exhibit enhanced dechanneling and narrower critical angles than the host crystal. MeV ⁴He backscattering spectra along <111> in twinned Si can be interpreted on the basis of additive contributions from host and twinned lattices.     

Coupling between precipitation and contact-line dynamics: multiring stains and stick-slip motion

The contact line in an evaporating drop can stay pinned to form a single ring or can shrink in a discontinuous stepwise manner and generate multiple rings. We demonstrate the latter with DNA solutions and attribute it to a pinning-depinning cycle that generates new contact lines. The new contact line recedes after depinning and is repinned at an internal precipitate ring that determines the location of the next contact line. Each precursor ring is formed when DNAs are trapped by an internal microstagnation flow and precipitation dynamics hence control this unsteady drop motion.     

Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams

For a light beam focused through a biaxial crystal along one of its optical axes, the effect of internal conical refraction in the crystal leads to the formation in the focal image plane of two bright rings separated by a dark ring. It is shown that, with circularly polarized Laguerre-Gauss LG(0)(?) beams entering the crystal, this classical double-ring pattern is transformed into a multiring one consisting of ?+2 bright rings.     

Electro-optically generating and controlling right- and left-handed circularly polarized multiring modes of light beams

We propose a simple method for generating and controlling right- and left-handed circularly polarized (RHP and LHP) multiring modes of light beams by means of Pockels effect in a single strontium barium niobate (SBN) crystal. The numerical results show that an LHP Laguerre-Gaussian LG(0l) beam, propagating along the optical axis of the crystal, will partly turn into an RHP vortex light field of order l+2. Moreover, a pair of the LHP and RHP components of the output light field is LG-like modes sharing an identically radial index, which is electro-optically controllable. The power ratio between these two components depends on the applied electric field and the mode of input beam.     

涡旋轴对称化的分形维数表征

涡旋轴对称化是影响热带气旋预报的重要动力学过程．截止目前的研究,均用等值线图形主观识别涡旋轴对称化．本文用一个准地转无幅散的正压涡度方程模式,数值积分48h,模拟了初始非轴对称涡旋演变为轴对称涡旋的轴对称化过程．根据模式输出数据,计算了逐时涡旋外缘线的分形维数DB,用分形维数DB的逐时变化客观表征涡旋轴对称化．在此基础上,计算了分形维数De与热带气旋尺度参数R。和热带气旋强度参数Vmax的相关系数．结果显示,DB与Rm的相关系数为-0．70,DB与Kmax的相关系数为-0．75,相关均显著．用此途径,客观表征了涡旋轴对称化与热带气旋参数的联系．结果在热带气旋预报中有应用前景．     

Vortex Flows Induced by Electric Arc

In this paper a mathematical model of the stationary electric arc is made on the basis of solution of radiation gas dynamics two-dimensional equations. Numerical analysis of electric arc with small length, depending on current force, distance between electrodes, electrode behaviour and geometry, type and expenditure amount of plasma forming gas, is carried out. It is shown that under some definite conditions electric arc induces toroidal gas vortexes playing an important part in the process of heat and mass transfer in electric arc plasma.     

Vortex core shapes measured by STM

We have studied vortex core shapes in superconducting NbSe₂ by STM, as function of temperature and bias voltage. The experimentally measured tunnel current profiles are compared with the results of calculations using microscopic theory. We find that, at low temperatures (T/T _c ? 0.25), the apparent vortex core radius strongly depends on the bias voltage, which demonstrates the energy dependence of the scale for spatial variation of the quasiparticle density of states. Good quantitative agreement between measured and calculated profiles is found by using the accepted value for the superconducting coherence length Ξ_S, without further adjustable parameters. This shows that the bias dependence is a useful extra tool in the interpretation of local density of states measurements.     

Selection and coexistence by reaction-diffusion dynamics in fitness landscapes

The phenomena of selection and coexistence are modelled as chemical pattern formation by competition for a given resource in heterogeneous spatial fields (fitness landscapes). The reactions form a closed reproductive cycle so that total concentration of species and their building-blocks is kept constant in time. Eigen's ‘constant overall organization' conditions can be view as a particular case of proposed conditions.

Species whose fitness values exceed the replication threshold govern the system dynamics. In the limit of vanishing diffusion of species and full diffusional mixing of resource, all individuals share a common niche and only the fittest survives during an evolution. In the opposite limit of negligible diffusivity of resource, there is no competition between individuals and all of them coexist. At the intermediate values of resource diffusion, a number of long-lived spatial niches are formed, which lead to long-term coexistence of locally fittest individuals.     

Vortex polarity switching by a spin-polarized current

The spin-transfer effect is investigated for the vortex state of a magnetic nanodot. A spin current is shown to act similarly to an effective magnetic field perpendicular to the nanodot. Then a vortex with magnetization (polarity) parallel to the current polarization is energetically favorable. Following a simple energy analysis and using direct spin-lattice simulations, we predict the polarity switching of a vortex. For magnetic storage devices, an electric current is more effective to switch the polarity of a vortex in a nanodot than the magnetic field.     

Constraint optimisation and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses such problems in the more familiar terms of optimisation in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard’ transition, and suggests an algorithm defining a new, higher, easy-hard frontier.     

Probing molecular free energy landscapes by periodic loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular, for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's relation for obtaining equilibrium quantities from nonequilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.     

Vortex nucleation by collapsing bubbles in Bose-Einstein condensates

Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.